[ODE] Euler vs. Runge-Kutta and adaptive step sizes

[nlin@nlin.net]

> I don't believe ODE is based on Stewart and Trinkle's time stepping
> algorithm, as described in the paper "An Implicit Time Stepping Scheme for
> Rigid Body Dynamics with Inelastic Collisions and Coulomb friction" because
> this paper uses position based inequality constraints, while ODE uses
> velocity inequality constraints, among other differences.  This basic
> assumption leads to a totally different problem that has to be solved, which
> is an NCP in the S+T paper.

The paper "Time Stepping for Three-Dimensional Rigid Body Dynamics", by
Anitescu, Potra, and Stewart seems to use a velocity-based LCP formulation
similar to ODE's. A note below Equation 7 says "Note that if M(q) is constant,
then (7) can be reduced to a linear complementarity problem..."

The Stewart/Trinkle paper with the title "Dynamics, Friction, and
Complementarity Problems" (which, however, has the title "Rigid body
dynamics with inelastic collisions" in the page header, so I don't know
actually what the real title of the paper is) is also velocity-based, as seen
in section 3.2. Here the authors mention that the formulation is an NCP,
which the authors say can be solved with iteration of LCP solutions to
converge to the nonlinear solution.

About half a year ago there was a fellow on this list who said he'd write
up a document describing in detail the derivation the equations used in ODE
(see http://q12.org/pipermail/ode/2001-November/000584.html), but I don't
recall hearing if any documentation was ever released by him or not.

Russ, can you provide a pointer to the specific paper(s) describing the
time-stepping formulation used by ODE?

> I agree with you that ODE's LCP solver is also integrated with its
> integrator to some degree, but this dependency can be easily removed (though
> I would not encourage doing that).

Why would you not encourage this?

-Norman